As I mentioned in my previous blog post, I have looked into and comprehended the ideas of Kurtosis and the least squares linear regression method.
The scatterplot’s relationship between variables is represented by the least squares linear regression approach. The method minimizes the sum of the squares and the vertical separation between the line and the data points while fitting the line to the data points. It is also referred to as a trendline or the line of best fit.
The linear equation, y = b + mx
Where, y = dependent variable
X = Independent variable
B = Y intercept
M = Slope of the line
To get the value of m, below formula is required
M = NΣ(xy) – ΣxΣy/ NΣ(x2) – (Σx)2
To get the value of m, below formula is required
B = Σy – mΣx/N
Where, N = Number of observations
- A statistical term known as kurtosis characterizes a probability distribution’s form. It offers details on the distribution’s peakedness and tails. Kurtosis aids in the analysis of a data set’s outcomes. The degree to which data values are clustered around the mean determines the peaking of a data distribution.Positive kurtosis denotes heavier tails and more peak distribution, indicating that the kurtosis is greater than that of the normal distribution, which has a kurtosis of 3.
A distribution with negative kurtosis has flatter tails and a lower kurtosis value than a distribution with a typical kurtosis of 3.
Kurtosis is equal to the normal distribution, which has a kurtosis of 3 and zero kurtosis suggests moderate tails and medium-height peaks.
In regression analysis, the Breusch-Pagan test is used to check for heteroscedasticity.
As reviewed in class today, the Breusch-Pagan test is used to determine whether a coin is fair, that is, whether it has an equal chance of landing heads or tails. If we choose to toss a coin 100 times and note the results.
There are two types of hypotheses, as follows.
Null Hypothesis (H0): The coin toss data do not exhibit heteroscedasticity, indicating that the variance of the results (heads or tails) is constant over all tosses.
Alternative Hypothesis (Ha): The statistics from the coin toss show heteroscedasticity, indicating that the variance of the results (heads or tails) may not be constant and may change from throw to toss.
- If the p-value is greater than significance level (e.g., 0.05), we do not have enough evidence to reject the null hypothesis. This suggests that the variance of the coin toss outcomes remains relatively constant, and there is no significant heteroscedasticity.
- If the p-value is less than significance level, we may reject the null hypothesis in favor of the alternative hypothesis. This implies that there is evidence of heteroscedasticity, indicating that the variance of coin toss outcomes may not be constant, and there could be variations in the coin’s behavior across the tosses.
